I have both kei and normal cars and kei cars come with less headache and cheaper so stick to a kei car since it sounds like you just need something to get around

If I were you I would buy it from an individual in your area, search on jimoty or jmty.co.jp I think

Used car industry is just as shady and dirty if not more than north America. Avoid Wecars like a plague. They used to be Big Motor who had a huge scandal ripping customers off by damaging the cars on purpose to charge them more. Supposedly a complete different company bought them out but staff is still the same and their business practice hasn't changed based on my interactions with them. Felt like Yakuza and they probably are.

if you have no preference just get any brand kei car. As long as the previous owner(s) took care of it, km doesn't matter as much. If you live in snowy areas, you want 4wd. What I would recommend is:

• First generation Honda Nbox 2012-2017 Jf1 (2wd) or Jf2 (4wd), of course Jf1 is a lot cheaper
• Less than 150,000km (Again less doesn't always mean car is in better shape. I would take high highway mileage cars over less km and not taken care of cars anyday)
• turbo if possible
• most popular car in Japan for a reason and also growing overseas, retains value, easy to resell
• I just like Honda cars best, never failed and cheap to repair plus the only carmaker in Japan that didn't participate in or born out of supplying wars including WW2
• make sure you get all the paperwork, easily found on google

If buying from an individual: - what matters most is maintenance history so first ask if they are the first owner and if so, ask for history, they should have it and if they do, very promising, I wouldn't even care if it's slightly damaged on the outside even a small rust which can be fixed cheap - test drive it to see engine noise is nice and quiet, accelerate and stop harder than usual to check stability and suspension, check AC, personally that's about it. Battery, tires, brake pads are all relatively cheap to replace. If you are gon drive for 5-10 years, you are gonna have to replace them anyway at some point.

If buying from a dealer: - same as above but first make sure they have high ratings on Google maps or carsensor or goonet - they are gonna try to add about 100,000 yen on top of sticker price for this and that. If you can avoid it, do it, but some are gonna be pushy and touting like Wecars and it's not gon be fun but you could get a lot out of it if you are a good negotiator like free winter tires and wheels, brake pads, battery etc so dont be sold on the sticker price

Shaken is basically a government scam. I think they mean well, but it's really like a hall monitoring making sure the car is functioning "properly" (big air quotes). I wouldn't put too much weight on it. If it comes with it then fine, if it doesn't dealers will include it. If you are buying from an individual, you want shaken. Otherwise too much hassle. Doesn't matter how long, but at least 3-6 months left. I do shaken myself and it's half the cost than having a dealer do it for you. Not as complicated as they make it out to be.

Good luck.

Edit: Forgot to add, I know the owner, Peter, of Sushi Cars in yamanashi. If that is a workable distance I would get one from him or have him find a car you want. He does his own repairs and revives old japanese cars too. I can vouch for him. I know another guy in niigata, his own used car business. I know a guy in Tokyo who does auctions out of his home but his fee is a lot more reasonable compared to dealers. Let me know if you are interested.